Search: id:A007482
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%I A007482 M2893
%S A007482 1,3,11,39,139,495,1763,6279,22363,79647,283667,1010295,3598219,
%T A007482 12815247,45642179,162557031,578955451,2061980415,7343852147,
%U A007482 26155517271,93154256107,331773802863,1181629920803,4208437368135
%N A007482 Number of subsequences of [ 1,...,2n ] in which each odd number has an 
               even neighbor.
%C A007482 The even neighbor must differ from the odd number by exactly one.
%C A007482 If we defined this sequence by the recurrence (a(n) = 3*a(n-1) + 2*a(n-2)) 
               that it satisfies, we could prefix it with an initial 0.
%C A007482 a(n) equals term (1,2) in M^n, M = the 3x3 matrix [1,1,2; 1,0,1; 2,1,
               1]. [From Gary W. Adamson (qntmpkt(AT)yahoo.com), Mar 12 2009]
%C A007482 a(n) equals term (2,2) in M^n, M = the 3x3 matrix [0,1,0; 1,3,1; 0,1,
               0]. [From Paul Barry (pbarry(AT)wit.ie), Sep 18 2009]
%D A007482 N. J. A. Sloane and Simon Plouffe, The Encyclopedia of Integer Sequences, 
               Academic Press, 1995 (includes this sequence).
%D A007482 R. K. Guy, Moser, William O.J.: Numbers of subsequences without isolated 
               odd members. Fibonacci Quarterly, 34, No. 2, 152-155 (1996). Math. 
               Rev. 97d:11017.
%H A007482 T. D. Noe, <a href="b007482.txt">Table of n, a(n) for n=0..200</a>
%H A007482 INRIA Algorithms Project, <a href="http://algo.inria.fr/bin/encyclopedia?Search=ECSnb&argsearch=442">
               Encyclopedia of Combinatorial Structures 442</a>
%F A007482 Let b(0)=1, b(k)=floor(b(k-1))+2/b(k-1); then, for n>0, b(n)=a(n)/a(n-1). 
               - Benoit Cloitre (benoit7848c(AT)orange.fr), Sep 09 2002
%F A007482 The Hankel transform of this sequence is [1,2,0,0,0,0,0,0,0,...]. - Philippe 
               DELEHAM (kolotoko(AT)wanadoo.fr), Nov 21 2007
%F A007482 G.f.: 1/(1-3x-2x^2). a(n)=3a(n-1)+2a(n-2). a(n)=(ap^(n+1)-am^(n+1))/(ap-am), 
               ap := (3+sqrt(17))/2, am := (3-sqrt(17))/2.
%F A007482 a(n)=sum{k=0..floor(n/2), C(n-k, k)2^k*3^(n-2k)} - Paul Barry (pbarry(AT)wit.ie), 
               Apr 23 2005
%F A007482 a(n)=Sum_{k, 0<=k<=n}A112906(n,k). - Philippe DELEHAM (kolotoko(AT)wanadoo.fr), 
               Nov 21 2007
%o A007482 (Other) sage: [lucas_number1(n,3,-2) for n in xrange(1, 25)] # [From 
               Zerinvary Lajos (zerinvarylajos(AT)yahoo.com), Apr 22 2009]
%Y A007482 Cf. A007455, A007481, A007483, A007484.
%Y A007482 Row sums of triangle A073387.
%Y A007482 Cf. A000045, A000129, A001045.
%Y A007482 Sequence in context: A089579 A166336 A002783 this_sequence A134760 A132889 
               A149061
%Y A007482 Adjacent sequences: A007479 A007480 A007481 this_sequence A007483 A007484 
               A007485
%K A007482 nonn,easy,nice
%O A007482 0,2
%A A007482 N. J. A. Sloane (njas(AT)research.att.com).

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